Hausdorff dimension of a random invariant set
type: Item
instance of: scholarly article
title: Hausdorff dimension of a random invariant set
zbMATH Open document ID: 0919.58044
DOI: 10.1016/S0021-7824(99)80001-4
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1999-09-07T00:00:00Z
review text: The author proves that, as in the case of the deterministic attractor, the Hausdorff dimension of the random attractor for a dissipative stochastic dynamical system can be estimated by using global Lyapunov exponents. The result is obtained under assumptions that are satisfied by many stochastic dynamical systems originating in dissipative evolution equations. As an application, the author considers a stochastic reaction-diffusion equation and shows that its random attractor has finite Hausdorff dimension.
reviewed by: Gianna Stefani
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 34D08
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 34D35
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 1268421
zbMATH Keywords: deterministic attractor
zbMATH Keywords: random attractor
zbMATH Keywords: dissipative stochastic dynamical system
zbMATH Keywords: Ljapunov exponents
zbMATH Keywords: dissipative evolution equations
zbMATH Keywords: stochastic reaction-diffusion equation
zbMATH Keywords: Hausdorff dimension
author: A. Debussche
MaRDI profile type: Publication
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Wikidata QID: Q127570811
description: scientific article; zbMATH DE number 1268421